Rational Expectations, or, The Road to Incoherence

J. W. Mason left a very nice comment on my recent post about Paul Romer’s now-famous essay on macroeconomics, a comment now embedded in his interesting and insightful blog post on the Romer essay. As a wrote in my reply to Mason’s comment, I really liked the way he framed his point about rational expectations and intertemporal equilibrium. Sometimes when you see a familiar idea expressed in a particular way, the novelty of the expression, even though it’s not substantively different from other ways of expressing the idea, triggers a new insight. And that’s what I think happened in my own mind as I read Mason’s comment. Here’s what he wrote:

David Glasner’s interesting comment on Romer makes in passing a point that’s bugged me for years — that you can’t talk about transitions from one intertemporal equilibrium to another, there’s only the one. Or equivalently, you can’t have a model with rational expectations and then talk about what happens if there’s a “shock.” To say there is a shock in one period, is just to say that expectations in the previous period were wrong. Glasner:

the Lucas Critique applies even to micro-founded models, those models being strictly valid only in equilibrium settings and being unable to predict the adjustment of economies in the transition between equilibrium states. All models are subject to the Lucas Critique.

So the further point that I would make, after reading Mason’s comment, is just this. For an intertemporal equilibrium to exist, there must be a complete set of markets for all future periods and contingent states of the world, or, alternatively, there must be correct expectations shared by all agents about all future prices and the probability that each contingent future state of the world will be realized. By the way, If you think about it for a moment, the notion that probabilities can be assigned to every contingent future state of the world is mind-bogglingly unrealistic, because the number of contingent states must rapidly become uncountable, because every single contingency itself gives rise to further potential contingencies, and so on and on and on. But forget about that little complication. What intertemporal equilibrium requires is that all expectations of all individuals be in agreement – or at least not be inconsistent, some agents possibly having an incomplete set of expectations about future prices and future states of the world. If individuals differ in their expectations, so that their planned future purchases and sales are based on what they expect future prices to be when the time comes for those transactions to be carried out, then individuals will not be able to execute their plans as intended when at least one of them finds that actual prices are different from what they had been expected to be.

What this means is that expectations can be rational only when everyone has identical expectations. If people have divergent expectations, then the expectations of at least some people will necessarily be disappointed — the expectations of both people with differing expectations cannot be simultaneously realized — and those individuals whose expectations have been disappointed will have to revise their plans. But that means that the expectations of those people who were correct were also not rational, because the prices that they expected were not equilibrium prices. So unless all agents have the same expectations about the future, the expectations of no one are rational. Rational expectations are a fixed point, and that fixed point cannot be attained unless everyone shares those expectations.

Beyond that little problem, Mason raises the further problem that, in a rational-expectations equilibrium, it makes no sense to speak of a shock, because the only possible meaning of “shock” in the context of a full intertemporal (aka rational-expectations) equilibrium is a failure of expectations to be realized. But if expectations are not realized, expectations were not rational. So the whole New Classical modeling strategy of identifying shocks  to a system in rational-expectations equilibrium, and “predicting” the responses to these shocks as if they had been anticipated is self-contradictory and incoherent.

19 Responses to “Rational Expectations, or, The Road to Incoherence”

  1. 1 Henry October 6, 2016 at 2:47 pm

    Brilliant insights all round.

  2. 2 Nick Rowe October 6, 2016 at 3:06 pm

    I think I disagree with some of this David.

    I can have rational expectations, and update my expectation rationally when new information comes in.

    My rational expectation can be different from your rational expectation, if I have different information from you.

    In both cases the expectations will be probabilistic; I won’t (rationally) hold any belief with certainty, if I know I don’t have full information.

    Game theorists don’t bother calling it “rational expectations”. They talk about Bayes-Nash (or something) equilibrium.

  3. 3 david w October 6, 2016 at 3:54 pm

    I thought the Expectation operator is the average expectation. The ‘Rational’ expectation was that the average expectation was the correct one, that not everyone has to have the right expectation all the time.

    But, it’s been a long time since I looked at this stuff.

  4. 4 David Glasner October 6, 2016 at 4:46 pm

    Henry, Thanks.

    Nick and david w, What concept of equilibrium are you using when you say that rational expectations can be consistent with conflicting expectations of the future? And by what criterion do we establish that an expectation is rational if it is not the future price? Isn’t that the criterion that Muth used?

  5. 5 Nick Rowe October 6, 2016 at 5:19 pm

    David: that sounds more like perfect foresight, which is only the same as rational expectations under full information.

    Take a simple example. Suppose you build a model where the price level is a random walk P(t) = P(t-1) + e(t) where e(t) is mean zero and uncorrelated (Actually, that’s pretty much what you get if the central bank targets 0% inflation.)

    An agent who knows the current price level would have a rational expectation of next period’s price level E[P(t+1)] = P(t)

    An agent who had worse information, and who only knew last period’s price level would have a rational expectation E[P(t+1)] = P(t-1)

    (That’s the crude version, that ignores the subjective uncertainty in their expectations.)

    Lucas 72 for example is a rational expectations temporary equilibrium model where agents don’t have full information (they can’t distinguish real from nominal shocks), and so get surprised about next period’s price level.

  6. 6 Philip George October 6, 2016 at 7:21 pm

    The trouble with all economic schools is that while they worry about the implications of an uncertain future they take no note at all of the certain past. For a person who has lost a large chunk of his net worth in an asset crash that past is what will determine his future for a very long time to come. He was irrational in the past (or at least his expectations got a rude shock) and he will have to compensate by being ultra-rational in the future, viz. by raising his saving rate in order to recover his lost net worth.

  7. 7 Henry October 6, 2016 at 8:16 pm

    “I can have rational expectations, and update my expectation rationally when new information comes in.”

    How can there be rational expectations if expectations are modified by new information?

  8. 8 Henry October 6, 2016 at 8:22 pm

    “My rational expectation can be different from your rational expectation…”

    It doesn’t work that way, does it?

    We are, qua economic agents, supposed to know what portends at all times (at least with a measurable mean and with a standard deviation).

  9. 9 Henry October 6, 2016 at 8:34 pm

    “My rational expectation can be different from your rational expectation”

    It is irrelevant in the realm of the REH that in the real world people, individuals, form their own expectations.

    In the realm of the New Classical Model, there is a representative agent – he faces an information future which is governed by a distribution (mean, standard deviation).

  10. 10 Greg October 7, 2016 at 12:35 am

    Forget the article, the comments say it all. You can’t agree on what an RE is, who or how many there are, or who’s allowed them…. Angels and pinheads.

  11. 11 JKH October 7, 2016 at 3:40 am

    Nice explanation.

    If your working definition of rational expectations is the right one, then your point about the contradiction inherent in any assumed unforeseen shock, while very interesting, seems logical and obvious enough. I wonder why it hasn’t been more generally recognized before. It would seem to be fundamentally problematic for the use of rational expectations in modelling.

  12. 12 Srini October 7, 2016 at 7:13 am


    Terrific post. This appears to be a general problem with Bayesianism.


    There is also a related literature, which argues the impossibility of simultaneously maintaining rational expectations and learning.


    Bottom line: the rational expectations hypothesis is problematic.


  13. 13 Unlearningecon October 7, 2016 at 1:30 pm

    This is a great post as always, David.

    There are a couple of similar issues that have always bothered me about macro models. I am entirely willing to admit that these may just be my misunderstandings and am happy to be corrected. As Greg has pointed out, this stuff is just confusing.

    – When you solve the transition path of a macro model after a shock, it is in steady state equilibrium at every point in the transition. So when does the adjustment actually take place?

    – You solve a model before a shock, which gives you the (steady state) maximisers of an infinite summation. Then after some t<inf, there is a shock. You now solve the model from 0 to infinity after the shock. But shouldn't we be looking at what happens at time t, given that the model has been 'running' for t periods prior to the shock? Would the relevant variables necessarily be at their steady state values values at time t? Does solving from 0 to infinity both times and speaking of the 'transition' between them really make sense?

  14. 14 Egmont Kakarot-Handtke October 11, 2016 at 2:51 am

    The road that turned out to be a blind alley
    Comment on David Glasner on ‘Rational Expectations, or, The Road to Incoherence’

    A paradigm is defined by its axioms. Orthodox economics is built upon this set of foundational hard core propositions: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub, 1985)

    The representative economist has not realized it but methodologically these premises are forever unacceptable. It should be pretty obvious that the neo-Walrasian hard core contains THREE NONENTITIES: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5).

    Nowadays, all scientists agree that angels, phlogiston, epicycles, superman, and the Easter Bunny are nonentities. As far as economics is concerned we can agree that utility, constrained optimization, intertemporal optimization, rational expectation, well-behaved production functions or supply-demand-equilibrium are nonentities just like the Easter Bunny. Every model that contains a nonentity is A PRIORI false. In practical terms: as soon a the word equilibrium/disequilibrium appears in an economic paper it can be thrown into the waste basket. The same holds for all other nonentities.

    The discussion of models that contain nonentities is vacuous. Nick Rowe, J. W. Mason and David Glasner resemble medieval witch hunters who exchange their opinions about the difference between incubus and succubus.

    Rethinking economics means to discard the failed paradigms and to fully replace Walrasian microfoundations and Keynes’s flawed macrofoundations by something new which has to be entirely FREE of nonentities. As Romer has recognized, with DSGE economics has hit the wall at the end of the blind alley.

    Egmont Kakarot-Handtke

  15. 15 I am Responding to Idiots October 13, 2016 at 8:06 pm

    There is a lot of ignorant stupidity in this post and the comments that follow. Egmont of course sets the record, but plenty of others contributed to making this webpage a festival of idiocy and ill-informed complaining. Glasner should read before making stupid comments and Unlearning Economics should just quit.

  16. 16 David Glasner October 14, 2016 at 8:51 am

    Sorry for having gone so long without responding. Let me begin with a more complete response to Nick and david W.

    Nick (1), You said:

    “I can have rational expectations, and update my expectation rationally when new information comes in.”

    I agree, but given the information available, there is only one rational expectation which is the equilibrium price vector that would obtain conditional on the available information. If the information changes, the equilibrium price vector changes and so would the rational expectation.

    “My rational expectation can be different from your rational expectation, if I have different information from you.”

    My information and your information cannot be true simultaneously. So if there are information differences, there cannot be a rational expectation, because at least one (and probably both) of us will turn out to be wrong.

    “In both cases the expectations will be probabilistic; I won’t (rationally) hold any belief with certainty, if I know I don’t have full information.”

    If people have, and act on, different information, their expectations can’t be rational, because their expectations will necessarily be disappointed. Given their expectations, there is no possible state of the world in which the expectations of anyone are realized. The fixed point property of the model – that when agents expect the equilibrium price vector their expectations are (or could be) validated — can’t hold.

    “Game theorists don’t bother calling it “rational expectations”. They talk about Bayes-Nash (or something) equilibrium.”

    Good for the game theorists, but they are talking about an equilibrium in which each agent assumes that other agents will adopt an optimal strategy, so that their expectations are consistent in a certain sense. Here we are talking about an underlying inconsistency in expectations that makes it inevitable that expectations are disappointed and then have to be revised.

    david w, That may be how some people interpret rational expectations, but I don’t understand what kind of mechanism could possibly operate to cause the average expectation to be rational. That is pure hand-waving. The supposed gain in realism doesn’t make the model more realistic, it’s a cosmetic concession, but it undermines the basic logic of the rational expectations method. Rational expectations should be thought of as a check on the internal consistency of a model, not as an empirical statement about the world.

    Nick (2) You said:

    “that sounds more like perfect foresight, which is only the same as rational expectations under full information.”

    It’s not perfect foresight, because I don’t rule out the possibility that everyone’s expectations are wrong. I am just saying that their expectations are consistent, so that there is some possible state of the world in which their expectations could be realized. If expectations are inconsistent, there is no possible state of the world in which anyone’s expectations are realized. Even if the expectations of some people are realized, their expectations are not rational because the actual price vector that validates their expectations is not an equilibrium price vector, but rational expectations are defined in terms of the equilibrium price vector. If everyone expects the equilibrium set of prices, then, as long as there is no exogenous change invalidating the information on which they based their expectations, their expectations will be realized.

    “Lucas 72 for example is a rational expectations temporary equilibrium model where agents don’t have full information (they can’t distinguish real from nominal shocks), and so get surprised about next period’s price level.”

    Lucas 72 was a failure which is why Kydland and Prescott invented RBC theory. But they just made a bad situation worse. Much worse!

    Philip, There is no reason in principle why the situation you are talking about could not be taken into account by any of the standard models, but to do so they would have to acknowledge that people act on different information and that the expectations on which they base their decisions is often very much mistaken. An economy can continue to function fairly efficiently within a certain range of error, but when expectations are too far off, the economy gets into trouble and the adjustment to past mistakes becomes very messy.

    Henry, You asked:

    ”How can there be rational expectations if expectations are modified by new information?”

    Expectations are rational if they are mutually consistent and could be realized in some possible state of the world. If it turns out that the actual state of the world is different from the state of the world that would have allowed those expectations to be realized, the expectations were rational, but they were incorrect.

    Greg, No, it’s all very simple really.

    JKH, Thanks. Obviously, I agree with your assessment of what I wrote and I share your impatience with the modeling strategy that has taken over macroeconomics.

    Srini, Thanks and thanks for the links.

    Unlearningecon, Thanks. I don’t agree that we can make any statement about the transition from one equilibrium path to another. The transition is terra incognita. Usually the assumption is that the new information is processed and there is an immediate jump from one path to the other. If you try to model the transition, you get into all the difficulties associated with the inconsistency between rational expectationse and learning, not to mention the intractable problems associated with trading at disequilibrum prices.

    I am Responding to Idiots, Thanks. Your indulgence is truly Trumpian in its humility and magnanimity.

  17. 17 Jerry Brown October 15, 2016 at 12:11 pm

    David Glasner- “Thanks, Your indulgence is truly Trumpian in its humility and magnanimity.”
    Absolutely awesome. I have been laughing for 10 minutes and just hope I never write something that merits Glasner’s criticism. And I had been worried that economists had no sense of humor. I am so happy I read to the end of your responses there. Thank you David Glasner.

  18. 18 B Cole October 23, 2016 at 5:15 pm

    Great post.
    Are macroeconomic models just politics in drag?

  1. 1 Links for October 14 | J. W. Mason Trackback on October 15, 2016 at 5:39 am

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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